a) A random variable, X, has the following probability density function: f(x)=\left\{\begin{array}{ll}

x / 5 & \text { for } 0 \leq x<2 \\

(20-4 x) / 30 & \text { for } 2 \leq x \leq 5 \\

0 & \text { otherwise. }

\end{array}\right. 1. Sketch the graph of f(a). (The sketch can be drawn on ordinary paper - no graph paper needed.) ii. Derive the cumulative distribution function of X. iii. Find the mean and the standard deviation of X.